Indicating apparatus



Dec. 16, 1952 D. A. ALSBERG ErAL INDICATING APPARATUS 7 Sheets-Sheet l Filed Deo. 14, 1948 S .Ql

.uk aux. .83ML W D. A. ALSBERG /NVEN To e. f? MuH/.STEFF U N T T A Dec. 16, 1952 D. A. ALSBERG ET AL 2,522,127

INDICATING APPARATUS 7 Sheets-Sheet 3 Filed Dec. 14, 1948 F/Ga 20" DIFFERENT/AL 7. Z5

DE TEC TOP MONITORING DIFFERENT/AL PHASE AT TURA/EV Dec. 16, 1952 D. A. ALSBERG ET AL INDICATING APPARATUS '7 Sheets-Sheet 5 Filed Dec. 14, 1948 alililililil D. A. ALSBERG /NVENTORS' f R. l? MUHLSTEFF ATTORNEY Dec. 16, 1952 D. A. ALSBERG ETAL INDICATING APPARATUS 7 Sheets-Sheet 6 Filed DeO. 14, 1948 o. ,4. ALsERc NVENTORS' R. P. MUHLSTEFF @6x- Q-Qoeu ATTORNEY Dec. 16, 1952 D. A. ALSBERG ETAL 2,622,127

INDICATING APPARATUS Filed Deo. 14, 1948 7 Sheets-Sheet 7 z, 1k E Z2 l1'/ F I6.' /9 i Z Foule l E: TERM/NAL E4 Z2 E2 E lvrrwonk aA. ALsERc Nm/7355 RP. MUHLSTEFF OM gm A TTORNEV Patented Dec. 16, `V1952 UNIT-ED STI'ATE'S PATENT O'FFI CE v-2,622,127 iNIo'rING APPARATUS Dietrich A. Amberg, {Berkeley- Heights, N. VJ., f and Roberti?. YMuhlpsteff, New York,-'N. Y.,jassigno rs to Bell Telephone Laboratories, `Incorporated,

New York, N. 'Y-a corporation of New York .1 This invention'relates to afmethod'of-"and system for measuringthefphaseshift and theltransmissionv of electrical 'apparatusfand more specically to a movable indexforusein; such measuring method and system. "While"the-invention vis described in connection'yvithmeasuring apparatus, it has other applicationsas will'be'hereinafter mentioned. l l

One known type offcircuit fonmeasuringthe insertion phase shift' of an apparatus under test involved the procedure of (a) rstly,"'substituting a short circuit for the apparatus 'under test 'and then adjusting a calibrated phase shifter ofthe circuit'until la zero reading Was-provided on 'a suitable indicator whereupon the phase shifter would show A degrees; and secondly, replacing the Vshort circuit with the apparatus under test and then adjusting the calibratedfphase'shifter until the zeroreading'vvas reestablished on'the indicator whereupon' the phase'shfter would' now nread B degrees. The insertion phase'shif't ofthe apparatus under test would" then be (B"-A) degrecs. Such subtraction lWas vcinnbersor'ne and tended toward algebraic errors on the party o'fthe operating personnel. Also,in the past,` oney phase 'shifter lwas used vto. provide the A reading, and

therefore a second phaseishifter Wals. required to establisha direct' indication ofthe (BL-'21.) *reading. t l l Now, let it be assumed,that'there-'lrasfbeen' devised a perfect pl'iase-shifterr"calibratedl 'with a 'linear scale and lVariable "continuously 'through 36o-degrees by'rotation' ofjazfshaft. ,"S'u'c'h linear scale'could be coaxiallymountedwith theishaft and adjusted in 'position independentlythereof. The initial zero balance `ofi the "system could` then Abe established by movingthe fs'haftof'l the phase shifter through'A degrees, 'and thereafter rotating the linear scale untirits 'Zerop'oi'ntcorresponds exactly with ra fixed index' serving Aasfa 40 reference point. Thereafter, -whenf the Jcircuit with Vthe assumedphase v).shifte'rfand linearscale is lutilized to measurethe insertion phaseshift of the apparatus undertestjthe'linear'scaled/ill such deviationvfere incorporated' inftlief'scaiathe latter would becomenon-linean *Asia -cilse quence, it vwould be no longer: 'possible to moveA the scale relative to `the-.phase shifter shaft, as such n movement would destroy the calibration.

The 'present invention contemplates aidi're'ct reading system `With linearscales for measuring 'pliase'shift' continuously through 360 degreesby utilizingfa" movable index? for automatically compensating 'such system for' deviations fromlin- 'earty The main''objectr ofthe invention'is to provide afsystem for directly indicating phase'mea'surements.

Another object `is'to provide a'movabl'efindex for a direct-reading phase measuring system' having linear scales.

`Afurtherfobject -is toprovide a directreading phase' measuring systemwith` an' over-all 'zero at -Whichzthe measuring 'scales' thereof are adjustable to 'zero to represent the over-all system'zero.

A further object is to derive a-primary standard of phase' shift which is subm'ultiple--of v360 degrees.

Another object is to provide'-adirect-reading phase measuring' system with a-xed correction curve for residual errorl but `With= scales. adjustlable relative to the xed correction 'curve Another object is to provide calibrated' appa- 4ratus With a "movable `index y for indicating its deviatin'frmalpredeterrninedscale. Y

Another Objectis tof-simplify vthe utilizat'in-of moving indices With calibrated apparatus.

J1n4 a 'specific embodiment, the invention coinprises a photographic film containing acoiretin curve for the residual error of electrical'nieas'ring apparatussay, for example,` a calibrate'dp'hase shifter Y comprising a Vcondenser adjustable continuously through 350 degrees -bythe movement of-a.i rotor controlled by-therotation offagshaft. The Yfilm is mounted ifn'a predetermined position on the periphery of atra-nsparentfdrum Which'is fi-xedlyamounted'V coaxially nWith the phase shifter shaft. Abearn of light passed through the' 'drum anda portion of vthe correction curve thereon is projectedA onto a"screen` disposed adjacent "a" linearly` calibratedifine' scaleconnectedto the' shaft and representingone' vdivision ofi' a` secondliiiearly 45 calibrated 'coarse scale 'mounted coaxaily VTwith the shaft. The projected beambflight vmoves always present intheiphaserfshiftfcubration. If 5o at dfferentpostons 0f its rotr thr'ush the'SSO degrees shift effected thereby, s-uchcentralpoint 'representingno residuarerror. "The 'ene scale is read"a".f,`f'a-ir`1`st the light projection on the screen which constitutes a movable `index therefor.

A feature concerns the use of a movable scale with a calibrated oscillator or other calibrated apparatus. Another feature involves the establishment of a primary standard of phase shift, which is a submultiple of 360 degrees, and its transfer to apparatus to be calibrated.

A feature includes the provision of a directreading phase measuring system having linear scales and an automatic compensation for the residual error thereof. Another feature is that a change of calibration necessitates only a removal of the old film containing the correction curve for enabling the automatic compensation for the residual error of the system and the replacement thereof with a new film bearing the new correction curve. Another feature concerns the initial establishment of a fixed relationship between the correction curve and rotor of the phase shifter whereby the coarse and fine scales thereof may be adjusted to different relative positions therebetween Without disturbing the initial relationship of the correction curve and phase shifter. Another feature involves the establishment of a zero condition in the over-all phase measuring system whereat the coarse and ne scales of the phase shifter can be adjusted to zero reading without adversely affecting the relationship `between the correction curve and phase shifter. A further feature is that the directreading aspect reduces the tendency of operating porsonnel to make errors in the algebraic computations required by prior art phase measuring systems.

The invention will be readily understood from the following description when taken together with the accompanying drawing in which:

Fig. 1 is a box diagram of a system for measuring the transmission and phase characteristics of an unknown apparatus;

' Fig. 1A is a circuit modification that may be substituted in Fig. '1;

Fig. 2 is a box diagram showing a conventional arrangement for Calibrating, with reference to a standard phase shifter, a phase shifter used in Fig. 1;

Fig. 3 is a box diagram showing an arrangement for calibrating, with reference to an absolute standard of phase, a phase shifter used in Fig. 1; Y

Fig. 4 is a schematic circuit showing a fundamental concept of the differential phase detector used in Fig. 1;

Figs. 5 and 6 are vector diagrams of certain phase relationships obtainable in Fig. 4;

Fig. 7 is a schematic circuit showing the basic type of phase detector used in Fig. 1;

' Fig. 8 is a modification of Fig. 7 and is a schematic circuit showing the differential detectors for measuring transmission and phase in Fig. 1;

Fig. 9 is a schematic circuit of an arrangement for vproviding the phase and transmission indicators in Figs. 1, 7 and 8, with coarse and fine scales;

Fig. 10 illustrates the dial arrangement for the calibrated attenuator used in Fig. 1;

Fig. 11 is a schematic circuit showing an illuminating arrangement used for measuring gain and/or loss in Fig. 1;

Figs. 12, 13 and 14 delineate mechanical arrangements of an optical cam associated with a phase shifter in Fig. 1;

Fig. 15 is a modification of the arrangement shown in Fig. 12;

Fig. 16 is an alternate embodiment of the optical system shown in Fig. 12 and usable in Fig. 1;

Fig. 17 shows an optical system associated with a one scale measuring system Fig. 18 is another embodiment of an optical system usable in Fig. 2; and

Fig. 19 are schematic circuits defining measurements obtainable with Fig. 1.

In the following description identical reference numerals are utilized to identify the same elements appearing in the several figures of the drawing.

OVER-ALL MEAsURrNc CIRCUIT Fig. 1 illustrates a system for measuring insertion phase shift and transmission vthrough unknown apparatus under test I0 and may be modified by substituting Fig. 1A to the left of line 2 2 in Fig. 1 for measuring transfer transmission and transfer phase shift. Insertion phase shift and transfer phase shift difference may be dened by referring to Fig. 19 in which Fig. 19A comprises a source of voltage E having an impedance Z1 and connected to load Zz across which is a voltage Ei; and Fig. 19B comprises a source of voltage E having an impedance Z1 and connected to the input terminals of a generalized four-terminal network whose output terminals are connected to load Z2 across which is voltage E2. A voltage E3 occurs across the input terminals of the four-terminal network; and a voltage E4 appears across the output terminals of the latter network. Insertion loss and gain is defined as the ratio of voltage E1 to voltage E2 in Figs. 19A and B; insertion phase shift is defined as the difference in phase between voltages E1 and Ez in Figs. 19A and B. Transfer transmission is defined as the ratio of voltage E3 to voltage E4; and transfer phase difference is defined as the difference in phase shift between voltages Ea and E4.

In the system of Fig. 1, an oscillator I I of wellknown design supplies (1) a testing signal f of a frequency varying from 50 kilocycles to 3,600 kilocycles through an attenuator I2 to a resistance splitting pad I3; 2) a second signal f1 having a fixed frequency of 15,000 kilocycles to a synchronized oscillator I4; and (3) a third signal f2 varying in frequency from 11,400 kilocycles to 14,959 kilocycles to one input modulator I5. The oscillator I4 also supplies to a second input of modulator I5 a signal f3 having a fixed frequency of 15,031 kilocycles as disclosed in the copending application of D. Leed, Serial No. 65,130, filed December 14, 1948.

The splitting pad I3 is so arranged as to divide the testing signal f into two equal voltage portions of which one portion is supplied through the apparatus under test I9 to the input of a modulator I5 while the second portion is supplied directly to a modulator I l, both modulators being of a familiar design. The second inputs of modulators I6 and I7 are also supplied from the output of modulator I5 and through an attenuator I8 with waves f4 whose frequences vary from 81 kilocycles to 3,6'31 kilocycles. The output of modulator I6 is supplied through a calibrated attenuator I9 to the unknown input, as the test signal of the unknown branch, of a differential detector 20 comprising a differential phase detector 20a whose output is connected to a phase indicator 2| and a differential transmission detector 20h whose output is connected to a difierential transmission indicator 25 for effecting phase and transmission measurements, respectively, of the apparatus under test I0.

The output of modulator I1 is supplied through attenuator 22, calibrated phase shifter 23 to the standard input, as the test signal of the standard -i-nafter.

ential transmission ldetector .2017, Figs. V1 'and 8, to :modulator I5, Fig. l, for a purpose that Will be hereinafter mentioned. Thediiferential detector 20 and indicators 2| 'and 25 will also be hereinafter explained in connection with Figs. '7, and

9. A mechanical connection 32 vextends between attenuators I2 and'2-2, and anelectricalconnection 333 extends Abetween attenuators I2 and I9 forpurposes that will appear hereinafter.

`GALIBRATION or PHAsESniFTERQSIN FIG. 1

'For the purpose ofachieving a 'measurement ofthe insertionphase shift of theapparatus `11nder test :In in Fig. y1, there isemployed a phase shifter .223 of the well-known four-quadranttype having a rotor for varying phase continuously through 360 degrees as illustrated in Fig. 12. In

this connection it will be understood that other well-known types of .phase Shifters could be alternately utilized. As a perfectly linear phase shifter is normally unobtainable, vit is necessary to 'calibrate the phase shifter 23 yin order-to note the deviations from linearity through 360 degrees a'generator 21 of signal waves having a predetermined frequency'is connected to a splitting resistance pad 2B from whose output one `portion is applied through a phase shift standard -29 to the standard input of a differential phase detector 20a. rIhe other output Iportion from split- `ting pad 2S is applied through phase shifter 23, which is to be calibrated, to-the unknown input of the differential detector-20a. A suit-able indicator 2l connected to the output of differential phase ldetector 28a measures the difference between the vectorial sum and difference of the standard and unknown voltages applied to the input thereof as will be des-cribed in detail here- Thus, the phase shifter 23* may be calibrated in an obvious manner by comparison with the standard phase yshifter 29 in order to ascertain the deviation from linearity of the phase shifter 23 ateach point inthe calibration through 360 degrees.

I-Ieretofore, vthe phase shiftfstandard y29 in Fig.

.2 was defined by l, measuring the reactance and the resistance of astandard network and computing phase shift from such measurements; 2, using the sum and difference method of lphase measurement which defines 'phase shift in terms of voltage ratios; 3, utilizing a measurement of portions of a wavelength such as possible with llecher wires; and 4, pulse measuring devices.

A difliculty with all such prior arrangements was that inaccurate measurements tended to result as the vmeasuring rfrequency increased.

vInstead of using a derived standard phase shifter 29 as in Fig. 2, an absolute standard of phase may be determined by use of the lcircuit shown inFig. 3. This determination is absolute or primary in the sense that phase shift is defined directly without reliance on `externa-1 standards defined by frequency, or reactance, etc., such, for example, Vas in the case -of the standard phase shifter 29 in Fig. 2.

vThe arrangement of lFig. 3 about to be vdescribed is not limited by -frequencypandis equally effective at -a frequency vof l-O `cyclesfas well asv-at Ythe frequency of LOGO-megacyclesor-higher. 'I-o effect the phase determination of Fig. 3, it is only auxiliary networks and the apparatus to be calibrated be sufficiently stable; vand that'the error due to cross-talk andrpick-up in 'the'system involved be sufliciently small.

The basic method of Fig. 3 is one of successive approximation and is most `readilycomparable to the problem of subdividing a circle with a compass. Let it be supposed that the circumference of a circle is to -be subdivided into three equal arcs, each rof degrees. First,a startingpoint on the circumference `of the circle is arbitrarily selected and then the'compassis adjusted to Vspan 120 degrees. Commencing at lthe arbitrary starting point, three steps 'are vmeasured 'olf on the circumference of the circle with the compass. Assuming the compass 'spans exactly 120 degrees, the third step would 'return tothe arbitrary's'tarting point. 'If not, the spread of the 'compass is changed and the attempt to subdividethe circumference of the circle into the three equal arcs is repeated in a series of Aapproximations until finally the arbitrary starting Y*point is reached. Then, each 120-degree arc is divided into three equal arcs, each of 4() degrees. Thus, effecting the subdivisions by a factor 3 tends to reduce the cumulative yerror which would tend to be present if the `subdivision of the circumference were attempted by a higher factor say 9, for example.

In the circuit of Fig. 3, a generator 32! -of signals having a predetermined frequency is "connected through asplitting pad *35 having one terminal connected to -a phase shifter 23 to be calibrated and its opposite vterminal connected to a continuously variable uncalibrated phase shifter 37. The phase Shifters 23 and 3'! are continuously adjustable through 360 degrees, the former having its output applied through a variable attenuator 38 to one 'input of differential phase detector 2da whose output is connected to phase indicator 2i. rThe output of phase shifter 31 is connected through double-pole doublethrow switches itl, Yi2 and i3 in tandem, with which are associated adjustable phase shift networks de, 45 and 4S, respectively, `and lshort-circuiting straps il?, i3 and 49, respectively, and a variable attenuator 5i) to a second input o f the phase sensitive detector 20a. The networks 46, 45 and 46 are adjustable to provide phase shift to the amounts of degrees,9.0 degrees and 60 degrees, respectively.

The differential phase detector 2da, is relatively insensitive to the amplitude variations of the two Voltage inputs thereto but highly sensitive to unequalities of the vectorial sum and difference of the two voltage inputs thereto. The phase indicator 2| displays phase shift on a direct-reading scale in the following manner: The equation for indicator 2I is where D is the deflection; A is a scale factor; and F( i is the phase law of differential kphase detector 2da. If a scale conforming tovEquation l is affixed to indicator 2 I, such scale will indicate phase shift correctly lif the scale factor A were adjusted to the proper value.

In the operation 'of Fig. 3 for the purpose of Calibrating phase shifter 23, the signal generator 34 is adjusted to the desired predetermined frequency, at which the .phase shifter 23 `is to be calibrated, such frequency-being 31ki locycljes for the purpose of this explanation. Attenuators 38 and are so adjusted as to permit differential Vphase detector 20a to operate at its proper level adjusted until a zero reading is again established on indicator 2| Switch 4| is again connected to the short-circuiting strap 41, and phase shifter 31 is adjusted to establish a phase change in the same sense or direction as the next preceding phase change effected by phase shifter 23 until a zero reading is re-established on the indicator 2|. Then switch 4| is reconnected yto phase shifter 44, and phase shifter 23 is adjusted in the same sense as in its next preceding adjustment until a zero reading is again established on indicator 2|. If the actual phase shift occurring upon the throwing of switch 4| from its shortcircuiting strap 41 to the phase shifter 44 were exactly 180 degrees, then phase shifter 23 should have returned to the initial arbitrary starting point.

Ordinarily such exact occurrence will not be the case. Now, estimating the amount of phase shift by which the return to the initial arbitrary starting point in the calibration of phase shifter 23 was missed as indicated by line scale |48, Fig.

12, the phase shifter 44 is adjusted by about onehalf such estimated amount, and the foregoing procedure for calibrating phase shifter 23 is repeated. In successive repetitions of the above Calibrating procedure, the amount of phase shift by which the initial arbitrary starting point on phase shifter 23 was missed will be progressively reduced until such amount is no longer discernible. Thus, an absolute 180-degree phase standard is obtained; and a phase shift of 180 degrees from the initial arbitrary starting point on phase shifter 23 is established from the first step of the calibration. Thus, the phase shifter 23 now has the two calibrated points of (l degree and 180 degrees.

As a second step in the calibration of phase shifter 23, the latter is returned to .the initial arbitrary starting point, the switches 4i, 42 and 43 are connected to the short-circuiting straps 41, 48 and 49, respectively, and Ithe phase shifter 31 is adjusted to provide zero reading on indicator 2|. Next, switch 42 is connected to phase shifter 45, and the phase shifter 23 to be calibrated is adjusted in the same sense or direction as 1t was in the next previous adjustment thereof until the zero reading is returned to indicator 2 Then, switch 42 is reconnected to its short-circuiting strap 48, and phase shifter 31 is adjusted until a zero reading is provided on indicator 2|. Again switch 42 is connected to phase shifter 45, and phase shifter 23 is adjusted in the same sense or direction as its next previous adjustment until a zero reading is established on indicator 2|. If the relative phase shift of phase shifter 45 were exactly 90 degrees, the phase shifter 23 would have returned to the 180-degree point established via the first step of calibration. Ordinarily, this will not happen. Estimating the amount by which the return to the 180-degree point failed,

' the phase shifter 45 is Varied by about one-half such amount, and the calibration procedure according to step 2 is repeated. From successive vrepetitions of this procedure, the amount of 8 phase shift by which the 180-degree point was missed will be progressively reduced until such amount is no longer noticeable. Thus an absolute SiO-degree phase standard is obtained. Following the basic procedural system described in above step l, the calibration of phase shifter 23 is established for every possible permutation such, for example, as 0 1- 90; and 180i90. The i-degree and 270-degree points thus obtained are checked against each other with the absolute 180-degree phase standard obtained in step 1. Now the phase shifter 23 has the four calibrated points of 0 degree, 90 degrees, 180 degrees and 270 degrees.

As a third step in the calibration of phase shifter 23, the basic procedure of step 1 is now utilized with switch 43 and the BO-degree phase shifter 4S associated therewith to subdivide each of the four QO-degreeV divisions, heretofore established on phase shifter 23, into three 30- degree divisions. Upon the completion of the third step of calibration, the phase shifter 23 will include twelve points of 30 degrees, viz., 0 degree; 30 degrees; 60 degrees; 90 degrees; 120 degrees; degrees; 180 degrees; 210 degrees; 250 degrees; 270 degrees; 300 degrees; 330 degrees; and 360 degrees (or 0 degree).

Obviously a progression of submultiples of 30- degree phase shifters, not shown, could be used to subdivide each l0-degree section. However, it is convenient to'utilize differential phase detector 20a and associated indicator 2| for such subdivision in the following manner. From Equation 1,

Adjustment of the scale factor A provides an eiective range from +5 degrees to -5 degrees, or a lil-degree phase shift standard, which, when properly subdivided on the scale of indicator 2| enables a further subdivision of each :22g the above Sil-degree sections of phase shifter As a fourth step in the calibration of phase shifter 23, the latter is set at the BO-degree point or a multiple thereof previously established; and then phase shifter 31 is adjusted until a -5 degree reading is established on indicator 2|. Next, phase shifter 23 is adjusted to provide a +5 degree reading on indicator 2|. Now, phase shifter 31 is adjusted to re-establish the -5 degree reading on indicator 2|. This procedure is repeated twice until phase shifter 23 has been adjusted through 30 degrees to the next adjacent point, which is a multiple of 30 degrees, as determined by indicator 2|. If the scale factor A were correct the calibration should coincide exactly with the previously established SO-degree subdivision or multiple thereof. If the calibration and the Sil-degree subdivision do not agree, the scale factor A is adjusted, and the foregoing procedure repeated until agreement is obtained. Thus, the phase indicator 2| may be utilized to establish two 10-degrees subdivision between each two adjacent points which are multiples of 30 degrees. Upon the completion of the fourth step of calibration, the phase shifter 23 includes the points 0 degree, 10 degrees, 20 degrees, 30 degrees, 40 degrees, 330 degrees, 340 degrees, 50 degrees, 360 degrees (or 0 degree).

As a fifth step in the calibration of phase sh1fter 23, the indicator 2| may be used in a manner similar to the fourth step to establish a 5-degree subdivision between each two adjacent IO-degree subdivisions. In this case the phase shifters 36 and 31 are adjusted between the readings` of -5 degrees and 0 degree, or +5 degrees and. i degree. At this state ofl calibration, the phase shifter 23 includes the points 0 degree, 5 degrees.,Y degrees, 15 degrees, 20 degrees, 25 degrees, 341()y degrees, 345 degrees, 35.0 degrees-, 355 degrees, 360 degrees (or 0 degree). As aasixthstep in the calibration of phase shifter 23, the indicator 2| may be utilized in the manner of the fourth and fifth steps to establish four 1- degree subdivisions between each two adjacent pointsv that are multiples of 5 degrees.l Upon the completion of the sixth calibration step', therefore, phaseshifter 23 will include the points Q degree, l'degree, 2- degrees, 3 degrees, i degrees, 5 degrees, 6 degrees, '7 degrees 354 degrees, 355 degrees, 356 degrees, 357 degrees, 358 degrees, 359 degrees and 360 degrees (or 0 degree). Ina practical case, it was found that calibration 1200.1 degree for each multiple of 5 degrees was satisfactory.

rlhus, the circuit of Fig. 3 shows the only components essential to the calibration system, viz., 1, a phase shifter to be calibrated; 2, a plurality ofy phase shift networks adjustable to the multiples desired in the calibration; 3, an uncalibrated phase shifter continuously adjustable through 360 degrees; and el, a detector including an" indicator for identifying one arbitrary phase relationship, viz., quadrature, between two alternating voltages as will be subsequently explained inv connection with Fig. 7.

TRANSMISSION AND PHASE DETECTOR 20 1N FIG. l

The purpose of the differential phase detector 26a shown in Figs. 1, 2 and 3, respectively, is to identify an arbitrary phase relationship, quadrature, between two alternating voltages and comprises a phase discriminator 2,4 that will now be described in connection with Figs. 4, 5 and 6.. A characteristic of phase discriminator 24 is that it shall be substantially insensitive to amplitudev variations ofl the two input voltages whose relative phase is to be compared. The differential discriminator 24 shown in Fig. 4 is essentially a Wheatstone bridge comprising four arms of equal resistors, and having each of its two opposite diagonals connected tio, one of the two input voltages E1 and E2 whose relative phase is to be compared'. The general phase relationship between the two input voltages E1 and Ez toV the bridge in Fig. 4 is illustrated in Fig. 5.

Let it be assumed that E1 Sin` (,w E2: S111 (mi USilFlsA Complex vectorial notation E1 sin (et+ @1);13'13161 E2 sin (wi-i- 552) Ewige,

10. Hence for -l- 7L1r where n is any integer including zero ES=ED Thus, the amplitudes of the resultant voltages Es and- ED are equal when the, relativeY phase angle 1i is equal to 90 degrees, 270 degrees, 450 degrees, etc.; and are independent of the amplitudes of E1 and E2 as shown in Fig. 6.

The bridge phase discriminator 2li in Fig. ll maybe used as a deflection bridge wherein the resultant voltages Es and ED may be utilizedto measure the relative phase thereof.

From Equaticnsz and 3,

Equation 6 represents the phase law govern.- ing the utilization of the bridge phase discriminator M. FromEquatior-is 4, 5 and 6 Freni trigonometry If Equation 6 is used to determine the phase angle I and error A@ is incurred when lmEilelEglf. The errorl A@ can beY computed ffroignv Equation- 9. As one illustration, aY change of 5 degrees from the relative. phase of deg-rees between input voltages E1 and E2 requires a ratio of 1.75 decibels therebetween to produce an error AA Ia=0.1"f.

The properties of the bridge phase discriminator 24 shown in Figs. 4, 5 and 6 n'iay be. surnmarized as follows:

1. Phase shifts of between two input voltage E1 `and E2 will be dais,-

'11 tinguished regardless of the amplitudes of those voltages: u

2. For relatively small departures from the relatively small amplitude diierences between the input voltages E1 and E2 will cause relatively insignificant errors;

3. Although equality of the resultant voltages nominally exists every 180 degrees, this is only true when the four resistance arms in Fig. 4 are exactly equal. If those arms are unequal, balance will exist for all where A is the departure angle from 90 degrees between input voltages E1 and E2; and

4. Either of the balance conditions mentioned in next preceding item may be used to identify phase shifts in multiples of 2r exactly, regardless of imperfections in the phase discriminator. This meets the basic prerequisite for the absolute method of phase subdivision described above under Calibration of phase shifter.

The bridge phase discriminator 24 according to Figs. 4, 5 and 6 is incorporated in the difierential phase detector 20a shown in Figs. 7 and 8 which will now be explained. In Fig. '1, E1 and Ez represent two alternating voltages whose relative phase is to be measured. Voltage E1 is ap- Y plied through preamplifier 55 to the vertical diagonal of bridge phase discriminator 24; and voltage E2 is applied through preamplifier 56 and transformer 51 to the horizontal diagonal of bridge phase discriminator 24. Output voltages Es and En from the bridge phase discriminator 24 represent the vectorial sum and difference of voltages E1 and E2, at the bridge phase discriminator 24, and are applied through buffer amplifiers 58 and 59 of identical gain respectively, to a differential rectification system comprising solid rectiers or unidirectional devices 60, 6|, '62, and 63; capacitors 64, 65, 66 and 61; and resistors 68, 69, 10,1|,12,13, 14 and 15.

When the output voltages Es and ED from the phase discriminator 24 in Fig. 7 are equal, and assuming resistors 12, 13, 14 and 15 are equal, then no direct current potential will occur across the points A-B and C-D in the output of the differential rectifier system. When the output voltages E1 and Ez from the phase discriminator 24 are unequal, then direct current potentials will occur in output of the differential rectifier system across the points A-B and C-D in equal magnitudes but opposite phase, the latter being due to the poling of rectiers 60, 6|, I62 and 63. The magnitudes of the rectied voltages are proportional to the difference in magnitude between the voltages Es and En. The rectified voltages are applied to the control grids of amplifier tubes 16 and 11 included in a differential direct current amplifier 18 comprising, in addition, a cathode feedback including fixed resistors 82, 83 and 84 and adjustable resistors 85 and 86; plate resistors 81 and 88, and a center-zero mil llammeter serving as the previously-identified phase indicator 2|. Resistors 89 and 90 provide biasing potentials for the control grids of amplier tubes 16 and 11. Capacitor 9| provides a highv frequency by-pass to ground at points C and A.

Adjustable resistor 86 is adjusted to establish the same flow of direct current through plate resistors 81 and 88 whereupon no current will ow through phase indicator 2| when the latter resistors are equal. Adjustable resistor 85 controls the amount of negative cathode feedback and thereby the gain of amplifiers 16 and 11 in equal amounts provided resistors 82 and 84 have the same amount of eifective resistance.

Now, let it be assumed` that buffer amplifiers 53 and 59 have the same gain. When the voltages Es and En are unequal, rectied direct current voltages will appear across the points A-B and C-D to cause an unbalance in the amount of space current flowing in the direct current amplifiers 16 and 11. This will result in a iiow of current in the phase Vindicato-r 2| whereby a corresponding deflection is produced on the scale thereof. If the scale were proportioned according to the scale law given in above Equation 1, and the Vfactor of proportionality A were adjusted properly by varying resistor 85, the phase indicator 2| would show directly the change in phase from the quadrature relation of voltages E1 and E2 at the input of the bridge phase discriminator 24. Thus, the differential phase detector 20a in Fig. '1 provides an arrangement for identifying a definite phase relationship, viz., quadrature at the input of phase discriminator 24, between two alternating input voltages, and to indicate directly on suitably calibrated indicator 2| any change in such relationship. f

Fig.-8 is essentially the same as Fig. 7 except the former includes certain features to be identified hereinafter for facilitating the use of Fig. 7.

Switches |01 and |08 serve to interrupt the signal voltages applied to the control grids of amplier tubes 16 and 11 thereby permitting adjustment of resistor 86 to establish equal space currents through the amplifier tubes 16 and 11 as previously mentioned. Voltage dividers 99 and |09 and ||0 and |02 serve to vary the sensitivity of differential amplifiers 16 and 11 via single-pole double-throw switches |63 and |04, respectively, whereby use of the fine and coarse scales of indicator 2| is permitted. For maximum sensitivity, the resistance of voltage dividers 99 and |09 and ||0 and |02 must be high. Very small amounts'of grid current in the amplifiers 16 and 11 flowing through the resistors of the respective grid circuits will develop corresponding grid biases. The amount of grid current flowing in the respective grid circuits may be the same or diierent depending on the characteristics of the respective amplifier tubes 16 and 11. To preclude change in bias and thereby the production of a false reading on the scale of phase indicator 2| when actuating switches |03 and |04 from the line to the coarse scale of phase indicator 2|, and vice versa,`the resistance of the grid circuits must be kept constant. This is achieved by making the resistances of resistors |00 and |0| equal to that of resistors 99 and |02. As the voltage dividers 99 and |09 and |02 and ||0 complete the direct current path from the points B and D to ground the resistors 68, 69, 10 and 1| may be omitted in Fig. 8, if desired. Single-pole singlethrow switch |05 enables a varistor |06 to be connected in shunt of indicator 2| whenever desired, The varistor |06 possesses high initial resistance for applied voltage of relatively low magnitude and decreasing resistance for applied voltages of increasing magnitude. Thus, the varistor IIlS will be substantially ineffective as a shuntV for relatively small deflections on the scale'of'phase indicator 2l but an effective shunt for larger deilections thereby permitting maximum sensitivity of phase indicator 2l for small departures from the quadrature relationship of input voltages E1 and E2, and low sensitivity of phase indicator 2l for large departures from such relationship. In the ideal case, it happens that E1=Ez, and

1/2 when the quadrature relation occurs between theinput voltages E1 and E2. For, the purpose off checking the circuit of Fig. 8, a single-pole single-throw .switchl 94%, is closed, and'single-pole double-throw switchesv e5 and Slt are moved to theircontacts H" and F, respectively. Via voltage dividersi and 9S; a voltage V5 is applied tothe inputs of buffer amplifiers 58 and- 59 and the gainl thereof is adjusted until no voltageappears across the points A-B and C--D assho-wn by aY zero deflection on indicator 2 I-.

Referring again to Fig. 8, buffer ampliers 55 and 56 are connected through buifer ampliers II5 and Il-; respectively, to the input of adifferential transmission rectication system 2521 which isidentical with the differential phase rectifcation system hereinbefore described as connectecl: to the output of amplifiers 5S! and 59 and which has its outputconnected to an indicator 215: similar to the phase indicator 2'! but calibrated in suitable transmission units. The differenti'al transmission detector Zb and indicator 25 serve` to measure the difference between the amplitudes of' input voltages E1 and E2. Singlepole double-throw switch II?)v enables the application of, equal. voltage inputs to buifer ampli fiers. H5 and II-S. Buffer amplier I2@ provides a monitoring voltage which may 'be suppliedto a meter; not shown, or which may be utilized for. an. automatic voltage control AVC in Fig. 1 as hereinlexplained.

Fig.v 9` shows in further detail the varistor Idd in Fig. 8: fior: the purpose of providing each of indicators 2.1 and 25 with a desired non-linear scale. Due. to manufacturing variations. of in-- dividual. rectiers, the individual. rectifiers I-IA, as. shown.` in Fig. 9, may be. connected directly toleads,V I'Z'I, and |22 via a strap I23, or via individual trimmer resistors IZ, or several rectie fiers I it may beconnected through onetrimmer resistor IE5. The resistors IBA and 125l serve to adjust the characteristicsof. individual varistors I'I'i.

ESSED OPERATION or lfm. l

(c) For'measurin'g loss or gain In the operation of Fig. l, the apparatus under test 10 is tested with the testing waves j which vary from. 5 0. kilccycles to 3500 lzilocycles, and which are supplied to, one input of eachsof, modll"V ulators I6 and IT. The other input of each of these modulators issupplied at the same time, with the waves, f4 varying from 8l kilocycles to 3631 kilocycles. Hence, the outputs of modulators; I and lli include a` component having a frequency ofll Klocyci'es at which the-phase-and transmission characteristics of the unknown and standard paths are compared in the differential'.

detector 2.0'and measured bythe indicators 2l 'andi 25connectedthereto.

The Aattenuators..I I 2. and 2,2. are individually. adjustable'to one of the otherv of' the two-,positions "O-decibel loss and; 4U-decibel'A loss, These attenuators are connected togetherv by the me.- chanicalconnection 32fin Figs. 1. and. ll so that when-.attenuator I 2 is in the. O-decibel lossfposi-r tion.. the-'attenuator 2 2 isin the' 4U-decibel loss?? position; and soithat whenattenuator I2`isin thev i-decibeliloss, position, the attenuator 22'l is in the- O-decibel loss position.

For effecting a null operation of Fig. l, zero center scales are provided onindicatorsZI and 251; av 4G-decibel input level is`r to be: supplied tothev differential detector 2.0 from each of the unknown and standard` branches; the'. insertion phaselshiftoffthe apparatusunder test lO-is read directly from thecalibrated phaseshifter'23 and: the^loss. origainfof thevapparatus undertest 10' is read directlyfromcalibrated attenuatorIB'.

The-standard branch comprises as xed tra-nsmission conditionsy (1i)v a 20-decibel gain-in modu-` lator ITI, (2) a 20'decibel loss in phase shifter 23, and (3) aaO-decibely loss forei-ther gainorloss` measurement'siby. means of (a) the 4U-decibelloss-position effectivev inV- attenuator 22 when the O-decibel loss position is. effective in attenuator i2 for: loss-measurements, or (vb)A the40decibel" lossy" position in attenuator- IZ-when the O-decibel' lossf position iseffective in attenuator 2.2l for gain-measurements. The unknown branch comprises as a iixed transmission condition (1 az-l-.ZO- decibel.. gain in modulator I Bf; (2) a O-decibel loss. or "4U-decibel loss due to position of attenuator I2 when` eiecting loss or gain measurements, respectively; (3) gain orV loss ofthe apparatus under test 10; and (Ll)y effective attenuation of calibrated attenuator I9. As` a consequence, an effective 60-decibel loss should be present in each of the unknown or standard branches whereby the Xed conditions in each branch should add algebraically at all times tothe two -40decibel input levels to diiferential de'- tector 2i);

Assuming for thefmoment that (a) apparatus under test 10 is removed from the circuit of'Fig. 1 and replaced with a suitable short-circuiting strap say, for example, a section of coaxial cable; (b) attenuator I2 is on the O-decibel loss point; and (c) attenuator 22 of the standard branch is on the "e0-decibel loss, then` calibrated attenuator I9 in the unknown branch will actually include a "S0-decibel loss to compensate for the +20-decibel gain of modulator I6 whereby a 40-decibel signal is applied to the unknown input, ofthe differential detector20. At-` the same time the standard branch will include +20- decibel gain inmodulator lI, 20-decibel loss in phase shifter 23, and L10-decibel loss in attenuator 2,2 whereby a iOrdecibel. signal, due to the attenuation of attenuator 22 alone, is applied to the standard input ofr the diiferential detector 20. As a consequence,` each of the three dials on attenuator I9; will read' zero as willi be hereinafter explained.

Assuming further for the moment that (an) the apparatus under test 10 is still removed from the circuit of Fig. l and the short-circuiting strap of coaxial cable is still substituted therefor, (b) attenuator I2 of the unknown branch is onits "4U-decibel loss point, and (c) the attenuator 22 of the standard branch is on its "O-decibel loss point, then calibrated attenuator I9 of the unknown branch will actually include 20-decibel loss (4D-decibel loss in the attenuator I2, +20- decibel gain in modulator I6 and Ztl-decibel loss in attenuator I9) to compensate for +20decibel gain in modulator I6 whereby a LIM-decibel signal is applied to the unknown input of differential detector 20. At the same time, a 4I-20- decibel gain in modulator I'I and a 20-decibel loss in phase shifter 23 enable a 40-decibel signal due to the 4G-decibel loss in attenuator I 2 to be applied to the standard input of differential detector 20. As aconsequence the three dials of attenuator IS will read "4D-decibel loss as will be hereinafter explained.

The three dials on attenuator I9 are adapted to show readings of gain or loss directly thereon as shown in Fig.' 10 in the following manner. These dials are so arranged with two concentric Vsets of calibration numerals adjacent the periphery thereof that the outer set of numerals reads gain directly and the inner set reads loss directly. The outer calibration on each dial is stamped in red numerals adapted to be illuminated for indicating gain as will be hereinafter explained, in the forward direction as the dials are rotated in a counter-clockwise direction while the inner calibration is stamped in white numerals for indicating loss, as will be subsequently described, in the reverse direction as the dials are rotated in a clockwise direction. In this connection, it will be noted that the outer cali-Y bration of the IO-decibel dial includes both red and white numerals as will be pointed out hereinafter. Thus, the three dials are`v arranged for so-called reverse reading of loss These calibration numerals will be illuminated for indicating gain or loss measurements as hereinafter explained in connection with Fig. 11. It will be noticedin Fig. 10 that the l0-decibel step is omitted from the 1.0-decibel dial. The attenuator I9 and its three dials are calibrated as follows:

10 db dial-Actual db loss in attenuator 1.0 db dial-Actual db loss in attenuator 19 0 l 3 4 6 7 8 9 Gain 0 1 2 3 4 5 6 7 8 9 Loss 9 S 7 4 3 2 l 0 0.1 db dial-Ac- I tual db loss in attenuator 19.- 0 0. 1 0.2 0.3 0. 4 0.5 0. 6 0.7 0.8 0.9 1. 0 Gain .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1.0 Loss 1.0 .9 .8 .7 .6 .5 .4 .3 .2 .1 0

Thus, attenuator I9 will read as a maximum:

GAIN

30.0 db'on the 10 db dial 9.0 db on the 1.0 db dial 1.0 db on the 0.1 db dial 40.0 db total y Loss 50.0 db on the db dial 9.0 db on the 1.0 db dial 1.0 db on the 0.1 db dial 60.0 db total An illuminating system shown in Fig. 11 is associated by electrical connection 33 in Fig. 1 with the three-dial attenuator I9 and attenuator I2, Fig. l, to indicate by a red pilot lamp 200 that gain is being measured or by a white pilot lamp 20| that loss is being measured. In addition, a white lamp 200a and a white lamp 20m are positioned immediately in back of the red and white color designations of the numerical calibrations of the three dials of attenuator I9, Figs. 10 and 11 as hereinbefore mentioned. Accordingly, in a manner to be explained subsequently herein, the red pilot lamp 200 and corresponding red numerical calibrations on the dials of attenuator I9 visually indicate that gain is being measured; and the white pilot lamp 20| and corresponding white numerical designations on the dials of attenuator I9 visually indicatethat loss is being measured. The circuit, as shown in Fig. 11, is arranged to indicate visually that gain measurements are being effected.

Referring now to Fig. 1l, panel 202 associated with attenuator I2 includes a manually operated switch 203 for adjusting attenuators I2 and 22 via mechanical connection 32 to the "O-decibel loss and -40'decibel gain positions, respectively, for measuring loss; or to the -40 decibel gain and "O-decibel loss positions, respectively, for measuring gain. The switch 203 also connects via electrical connection 33, battery 204 to the lamps 200, 20I, 200:; and 20Ia, depending on whether loss or gain is being measured. A microswitch 207, i. e., a single-pole double-throw switch actuated by a cam not shown, attached to the shaft of the 10-decibel dial, Fig. 11, of attenuator I9 effects a change of lamps as the measurements go from gain to lossj or vice versa, when the 20-decibel changeover point is passed in a manner that will presently appear. In achieving such measurements there is a point at which the measurements change from gain to loss and vice versa, whereby the lamps are caused to change from red 200 to white 20| and vice versa. The changeover point is determined by the 4U-decibel loss in attenuator I2 in the following manner.

Initially, the circuit constants of the unknown branch of Fig. 1 are preselected so that at all times, as above explained,

and of the standard branch of Fig. 1l are preselected so that at all times as above shown:

(1l) LlO-decibel loss in attenuator -lloss of phase 12 in the standard brauch shifter 23 60 db loss Thus, the -60decibel gain constants of the unknown and standard branches of Fig. 1 enable a 40-decibe1 gain signal to be applied to the 1'7 unknown; and standard inputs of differential detector 20- as above mentioned.

EXAMPLE N0. 1

l40-decibel loss +0-decibe1 gain 20 decibels in in attenuator 12 or loss attenuator 19 apparatus 10 Hence, the apparatus under itest 10` has neither loss nor gain; and either red or Ywhite lamps 200 and 200a or 20I and 20 Ia, respectively, are illuminated in Fig. 11.

60 db loss EXAMPLE No. 4

LiO-decibel loss -I- l-decibel gain 2l decibels in in attenuator 12 in apparatus 10 lattenuator 19 Thus, the apparatus under test 10 has +1- decibel gain since l-decibel attenuation must be added to attenuator I; and the red lamp 200 and white lamps 200m are illuminated in Fig. 1l.

EXAMPLE No. 5

40-decibel loss -I- 8-decibe1gain -I- 28 decibels in in attenuator 12 in apparatus 10 attenuator 19 Y Thus, the apparatus under test 10,has +8- decibel gainsince i3-,decibel attenuation must be added to attenuator i0; and the red lamp ,200 and white lamps 20M are illuminated in Fig. 11.

Therefore, the e0-decibel ,attenuator I2 insertable in the unknown branch in Fig. 1, in view of the over-all "L10-decibel gain and 6U-decibel loss measurable as previously pointed out, xes the changeover in readings' from loss to gain and vice versaat the decibels normallyin attenuator I0 whereat the apparatus under test 10 has neither loss nor gain as hereinbefore mentioned. Hence, whenattenuatcr I0 includes ac- 60 db loss 60 db loss 60 db loss GOdb loss tual attenuation of a value less than 20 decibels I the apparatus under .test `10 has loss and the white'larnps 2.0i and 20m are always illuminated in Fig. 11; and when attenuator I9 includes actual attenuation of a value-above 20 decibels the appar-atus under test lil has vgain and the red lamp 205 and White lampsilllaare illuminated. Thus, i

Setting of Actual loss Readings on 3 attenuator Lfllla' in attenuadials of attenu- 12 p tor 19 ator 19 Db Db Db 0 00. O 60. 0 00. 0 0 60. O 00. 0 60. 0 IOSS 0 35. 6 24. 4 35. 6 loss Thus, the three dials of attenuator I9 will directly indicate loss lin reverse,reading- Y 18 1n addition,- the three-dial attenuator I9 infFig. l: measures gain or` loss as 'followsz Setting of Actual loss Readings 011,3

- Gam inapattenuator 1n attenuadials of attenu- 12 params 10 tor 19 am 19 Db Db Db Db -40 00. 0 20. 0 00. 0 -40 40.0 60.0 40.0 gain 0 -20..0 40. 0 20. 0 loss 0 -10. 0 50.0 10. 0 loss -40 -|2().'0 40. 0 +20. 0 gain `measurements, attenuator I9 is adjusted to'balance the unknown and standard-signals-until'a zero-center reading isproduced on indicator'25. The loss or gain of the apparatus y-underftest .10 is read directly from the three dia-ls on attenuator I0 in the mannerpreviously.explainedi v`For apparatus under test-10 having gain', the'actual attenuation-of attenuator I9 increases as the Again of each apparatus increases `so asvto measure gainf and for tapparatus undertest l0-having loss, the actual attenuationof attenuator'IQdecreases as the loss oi such apparatus -increases-.so asl to `measure loss Errample No. 1.-Assumc tl-decibel gai-nVl or loss for apparatus under ytest'lO, then (a) The-attenuator I2 isadjusted to the "40- decibel loss position while the attenuatorr 22 is adjusted to the O-decibel loss position;`

(b) The white lamps '20| and-20w. -arelfilluminated;

(c) The-'attenuator 'IS 'readsfO-O-G on its 10- decibel, 1.0-decibelY and (ld-decibel ldials-,respectively, i. e., neither gain-snor loss;

'(d) The actual'attenuation' in attenuator `Iltis 20 `Ydecibelsrso -as vtcanullify lthe F20-'decibel lgain off-modulator IB;

(e) The unknown branch has 4G-'decibel' loss comprising 40-decibellossof attenuator I2,` -I-'20- decibel gain of modulator I0', and '20-decibel loss"y of attenuator I9; and

'(f) The standard branch has a L11G-decibel loss ccmprising ll0-decibel loss of attenuator I2 infunknown branch, -I-ZO-decibel gainof modulator I1. 20-decibe1'loss of phase shifter`23.

Therefore, the apparatus under test 10 has neither loss nor gain.

Example No. 2.-Assume -l-llLG-decibel Vgain for apparatus` under test 10, then (a) The attenuator I2 is `adjusted to the 40- decibel loss positions while the attenuator22 is adjusted to the -decibel'gain position;

(b) The red pilot lamp 200 and associated white lamps 200a are illuminated;

(c) The attenuator I9 reads 14.6-dec`ibel gain (1 on the 10-decibel dial, 4 on the 1.0-decibeldial, and 0.6 decibel on the 0.1-decibe1 dial) (d) The actual attenuation in attenuator I9 is 34.6 decibels comprising 30.0 decibels per theflO- decibel dial, 4 decibels per the 1.0-de'cibel dial and l0.6 decibel per the 0.1-decibel dial; y

(e) The unknown v4branch as L10-'decibel Vloss Vcomprising l-decibel loss of attenuator I2,

+l4-decibel'gain of apparatus under test 10, -|-20-decibel gain of modulator I6, and 34.6-decibel loss of attenuator I9; and

(f) The standard branch has LlO-decibel loss as identified in paragraph of Example No. 1.

Thus, the apparatus under test 10 is an active network.

Escample No. 3.Assume IO-decibel loss in the apparatus under test 10, then Y (a) Theattenuator I2 is on the O-decibel loss position and the attenuator 22 is on the 4C-decibel loss position;

(b) The white lamps 20| and 2!Ia are illuminated;

(c) The attenuator I9 reads lil-decibel loss (l on the l-decibel dial or 9 on the 1.0-decibel dial, +1.0 on the 0.1-decibel dial);

(d) The actual loss in the attenuator I9 is 50 decibels comprising 40 decibels on the lil-decibel dial, 9 on the 1.0-decibel dial and 1.0 decibel on the 0.1-decibel dial;

(e) The unknown branch has Liii-decibel loss comprising "O-decibel gain of the attenuator` I2, 10-decibel loss in the apparatus under test 10, F20-decibel gain of modulator I5, and 50- decibel loss of attenuator I9; and

(f) The standard branch has cl0-decibel loss comprising Ii0-decibel loss of attenuator 22 in the unknown branch, +20-decibel gain of modulator I7, and 20-decibel gain in phase shifter 23.

Example No. Velf-Assume 54.9-decibel loss in the apparatus under test 10, then (a) The attenuator I2 is on the O-decibelv loss position and attenuator 22 is on the 40- decibel loss position;

(b) The white lamps 20| and 20| a are illuminated;

(c) The attenuator I9 reads 54.9-decibel loss as follows: 50 decibels on the l-decibel dial, 4 decibels on the 1 0-decibel dial and 0.9 decibel on the 0.1-decibel dial;

(d) The actual loss in the attenuator is 5.1 decibels comprising 0 decibel on the 10-decibel dial, 5 decibels on the 1.0-decibel dial and 0.1 decibel on the 0.1-decibel dial;

(e) The unknown branch has LlO-decibel loss comprising O-decibel loss in attenuator I2, 54.9- decibel loss in the apparatus under test Il), +20- decibel gain in modulator I6, and 5.1-decibel loss in attenuator I 9; and

(f) The standard branch has the L.l0-decibel loss as identified above under item (f) of EX- ample No. 3.

In connection with the 1.0-decibel and 0.1- decibel dials of attenuator I9 shown in Fig. 10, it will be understood that each dial may include eleven steps in which event the maximum reading of the 1.0 and 0.1-decibel dials would be 10.0 decibels and 1.0 decibel, respectively, whereupon the maximum reading of the attenuator I9 would be 61.0 decibels; or that each of the 1.0-decibel and-0.1-decibel dials may include ten steps in which event the maximum reading of the 1.0- decibel and 0.1-decibel dials would be 9.0 decibels and 0.9 decibel, respectively, whereupon the maximum reading of the attenuator I9 would be 59.9 decibels. As a consequence, the circuit constants of Equations 10 and 11 would be 61.0 decibels for the SLO-decibel attenuator and 59.9

. decibels for the 59.9-decibel attenuator just mentioned.

(b) For measuring 'phase shift To achieve phase measurements in Fig. liwith the apparatus under test 10 connected 1n circuit, the phase difference lmay be read directly on phase indicator 2|. For null measurements the calibrated phase shifter 23 is adjusted to provide a zero-center reading on phase indicator 2 I,k and the amount of phase shift inserted by the apparatus under test 10 is read directly from the calibrated phase shifter 23. For these measurements, the first measuring step is to establish a zero for the over-all phase measuring system in Fig. 1 in the following manner. This is done by substituting a section of coaxial cable for the apparatus under test 10 in Fig. 1, or otherwise effectively substituting a short circuit for it, to achieve a null measurement. Next, phase shifter 23 is adjusted to establish a zero-center reading on phase indicator 2|. Now the coarse and fine reading scales |37 and |48, respectively, associated with the phase shifter 23 in Fig. l2 are slipped via their respective friction clutches as described hereinafter in connection with Figs. 12, 13 and 14, until both scales show a zero reading. 'I'his constitutes the over-all zero for the phase measuring system of Fig. 1. As a second measuring step, the coaxial line section is replaced with the apparatus under test 10, and using the null procedure, the zero reading is reestablished on phase indicator 2| by appropriate adjustment of phase shifter 23. The amount of phase shift introduced by the apparatus under 10 is read directly from the coarse and ne scales |31 and |48, respectively, of the phase shifter 23 in Fig. 12. This obviates the need for adding or subtracting readings as would be required with scales incapable of the slippage above mentioned.

Modulators I6 and I'I are constructed such as to have identical gain-versus-frequency characteristics. They are also constructed such that a linear relationship exists between changes in the amplitude of the input waves of frequencies f and f4 and the amplitude of the output waves of the difference frequency f4-f, or 31 kilocycles. Hence, by varying the amplitude of waves of frequency f4 the outputs of modulators I5 and may be changed by the same factor. The AVC connection shown in Figs. 1 and 8 maintains substantially constant the amplitude vof the standard input into the differential detector 20, thus compensating the gain-frequency characteristic of modulator I5 and modulators I6 and and changes in amplitude of waves of ,f at the splitting pad I3 because of possible reflections from apparatus under test arising from impedance mismatch. This Ipermits direct reading of the scales of the phase and transmission indicators 2| and 25, respectively, as herein described.

OPTICAL GAM For. CALrBRA'mD PHASE SHIFTER 23 1N FIG. 1

As the calibration of phase shifter 23 includes residual error at different points, its calibrated scale would be non-linear if the deviations due to such error were incorporated therein. This would mean that the calibrated scale would be fixed relative to an arbitrary point on the shaft on which the latter is coaxially mounted, and once the scale is moved relative to such arbitrary point, the utility of the calibrated scale would be lost. In the calibration of phase shifter 23 as explained hereinbefore, its calibrated scale is made linear and is associated with a movable index representing the amount of its deviation from linearity due to residual error, in the manner that will vnow be described.

Referring to Fig. 12, phase shifter 23 comprising -the iWell-known- .fouropiadrant*:sine condenser havinga rotor fand stators iis zafxed ato one end of shaft `|39 on which is mounted spiderv |3|, gear |32 -and va transparent drum l33.

Spider 'i |'3 showsin Fig. v13` anf arm 34. .attached i rigidly atfits center to the shaft|33 and adapted with a pair of shoes |35 on itsopposite'ends held in 'frictional engagement With` the inner` periphery vof afdrum |33'carrying onr itsouter periphery 10 degrees-eachin linear form. The-"scalefl31 provides a coarse `reading of the Ieffective phase thereto and 'fadaptedlwith -ten l1de'gree "divisions in a llinear' manner, representing =one of j the thirty-six vlll-degreev steps on coarse =scale-|31 as above mentioned. vThisfrictionalv engagement is illustrated inFig. 14"in"Which-a ffrictionplate i343 anchoring'adjacent en'dsiof spaced' rods |53 andll|5| -Whose opposite -e'nds are xedlyf-m'ounted in'a button |52. v-A compression spring |53engaging an inner surface o'ffbutton |52"servesto control the fri'ctonal 'engagement between the ne: scale( |48 `and plate |49. fBy, pushing button |52 in'vfa right-hand direction, the pressureV of friction plate |49 on -finescale |148 is` released: whereby the latter may berotatedrelative vtoshaft2|46 for a-purpo'sethat-*Will later appear;`

and vvat r the-same time *frictionplate M9 engages panel: w3c thereby-flockingshaft |46 against4 rotation.

a-'coarse-scale--I'31and-a fine scale |48 are associated-'With 'the -shaft |30. 'The-'gear' ratio between the coarse'f-and'n'e scales-|3'1 and |48 is lto 36 whereby v'the nescale |43 is caused 4-to make thirty-sixcompl'ete revolutions for each' complete l revolution 'of' the coarse scale |31 pr; in another aspect, the 'ne scale l|48 makes -one'cornplete revolution for each l0-degree-step"ofthe'coarsel scale L |31.

Whenl-vthephase Ashifter Y'23 -iwas calibrated in the manner' hereinbeforey explained; it 'Wasfound scale |48 did notalWays-fall' onv thesamev fixed index 'for' eachA pointT calibrated. VIt so happened that the '0-d'egr'ee orlli-degreefpointfofthe fine scale |48'. tended tofalltoltherright or'leftof the .,xed index f-as -well as occasionally thereon. This meant that the phase shifter "i2-3 had residual Aerrorvvtfhich vWas peculiar to itsv1 adjustf ment Yat a givenl instant.- Thus, 'the phase 'shifter'I 23 nhad-al different #index -for f different 1'adjust-- ments ltheref- -lwhereby- Verroneous readings tended '-tofresult. As aconsequence itwas found necessary`- toprov-ide a movable index :for the fine `scale yHi8 -in order tto compensate for the residual "-error of lt-he `v phase 4shifter ,"23` in ta' marmerthat Willnow' be described;

Referring-againitoFig. 12,"a *negative photographic' nlm 53-containi ng `a calibration curve ofitranspanentr drumfl33 .fia-.manner-,fthatewill 1 bel'mentioned-dater;` LAzbeam .of `lightifrom"..lightv sourcel |158; is .-"focussed by lens |59 :on aimirror`v |63 .z and mrojectedithereby)tthrough lthe calibration @curve V'11551. .afconsequenca a f. relatively short'raand narrow :strip :of illumination t6?, is 'projected' iontovfroste'd tfsurface .16| of 1.a '.transparent" i'window'l 62 :whichv .is positioned in v:proximity .zof fne :scale :a 43. Due tozthe. opacity r of lm |f5 -v'atY all .pointszbutr thef .calibrationfcurve it` is obviouszthatfthe s light .beam will pass only throug'hfthe:calibration curve |51 thereon.Y `As the frosted'surface `1|:3 llies .in i the same-vertical plane withilthatnoffthenescale|48, no parallax existsbetween the latter Yand the 1projected:por

tion fof the calibration Acurve 1F51. `It will be noticed that'athe beam of light-'emergesfrom the leftlhandside `oflen's |59 inapproximately par-fv allel`li`n`es is convenienti-'but notnecessary.

Itis only required:that :the divergence. orconvergen'ce: of rtl-ie beamv ofi light -be unaltered `after the '.calibrationcurve :|51 is fixed onthe transparent vdrum 1133.. Thus,r the projected #lightbeam.A |`63 onithefrostedsurfacef 6 IY ofA the transparent 'Window 5| 62 provides a shifting zero which represents-fthe residual error of phase shifter 23 for different adjustments 'thereof and which constitutes 4`afmoving index against whichl fthe ne scale |48 is read for achievinglthemeasurement kof insertion phase of apparatus under test Hl ashereinbefore'describedl in connection with Fig. 11;

In'lmaking `correction curve |51 inv Fig. `12, a strip of transparent lm or thelike, ynot shown,

- is initially applied to the periphery of transparent druml` |33, in thestea'd of l'm |56. -As a-starting point, the lcoarse and fine tscales |31 and |48, respectively, are set Aat their zero points; and a suitable mark is made 4on'the film and transparentdrurn |33 to indicate a point A common toea'ch thereof,-'Fig. 12', `for a purpose-that will become evidentsubsequently. Thereafter, the phaseV shifteri 23 lis calibrated inthe mannerhereinbefore explained. 'In this vcalibration it is necessary to-iaclju'st'the phaseshifter 23 at yeach pointv` calibratedfso f' that the 'O-degree'v or 5''degree orotherscale -division on 'fine scale |48 is yre,- ferred to'an index. Since thelatter'shifted or movedf-with reference to a'fixedf'index for different calibratedpoints-of phase shifter 23 as previously pointed out,'an ink dot is now'placed on ,the 'film in vsuch*- a Way that its kprojection onto thescreen |`6| isfadjacent to the desired Vsubdivision of' the "fine: scale |48.

Thus', thereffw'ill bean ink dot on the lm for each calibrated point. of phase shifter 23 to representfwhere fthe 0-degree or l-degree-point` fell; Hand `"for the' purpose lofv the present explanation, itisassume'd that" there will be an ink spotpnthe lm, lfor example, at each of the thirty-six IO--degreesteps calibrated on the coarsescale |'3-1."`Sincethe coarse `scale |31, transparent drum *|33 "-andne'scale |48 areactuated''by Ithe commonshaft `13|) las `show-n .in

fFig. 12, it Will 'be evident: that the transparent drum |33 makes-'one-revolution for each revolutionof the coarse scale |31'Whereas thene scale |48 made` thirty=sixirevolutions `for each .revolutionv of 'the "coarse scale`|31 as previously men- "Therefore, there will vte .at least thirty-six ink"dots'spaced"alongthe length of thejlm. on the transparent druml |33. Next,.the 'i-llm .is re.

4 movedfrom'the 'transparent drumA r33,- then laid on' afftat surface; and" the' ink dots' thereon connected together by a reasonablyheavy ink line with the aid cfa so-called French curve. The connected ink dots will constitute a curve whichA is approximately sinusoidal for each of the four quadrants through which the rotor passes in calibrating the phase shifter 23 through 360 degrees. Asa consequence, the over-all inked curve on the film will comprise essentially four sinusoidal curves connected together, each of the latter curves having a hill and a valley portion.

Finally, the over-all inked curve on the lm is photographed and the negative thereof constitutes the film I 56 on the transparent drum |33 while the four connected sinusoidal curves form the correction curve |51 on the film |56 in Fig. 12. The negative film |56 is applied to the periphery of -transparent drum 33 -so that the starting point A on the negative lm |56 is disposed precisely Vat the starting point A on the transparent drum |33, Fig. 12. Thus, a relatively short and narrow strip of illumination |63 from the lamp |58 will pass through the correction curve |51, but will be blocked by the negative portion of the lm |56 adjacent thereto. This strip of illumination |63 is projected onto the frosted surface |6| of the transparent window |62 and moves back and forth therealong to constitute the movable index for the fine scale |48 as above explained.

An important aspect of theforegoing optical correctioncurve is that both the coarse and fine scales |31 and |48, respectively, may be adjusted to any desired relation with respect to the rotor of phase shifter 23 and the correction curve |51 on the transparent drum |33. In this connection,- it will be noted that the rotor of phase shifter 23 and the transparent drum |33 are rigidly positionedv in fixed relation on the shaft |30 but the coarse scale |31 is rotatable relative to shaft |30 via spider |31 and the ne scale |48 is rotatable relative to shaft |36 via finger knob |41 and the plate |49 frictionally engaging the latter as pointed out previously. Hence, the coarse and ne scales |31 and 48, respectively, may be adjusted to any desired relative positions without disturbing the xed relation between the correction curve |51 and the rotors of the phase shifter 23 in Fig. 12. The latter ensures that the proper amount of correction is made at the same adjusted positions ofthe rotor of the phase shifter 23 irrespective of the actual reading of the coarse and fine scales |31 and |48, respectively. Hence, it will be noted that the correction for residual error is associated with the rotor and not with the coarse and/or ne scales per se. Accordingly, the relative movement between the coarse and ne scales performs essentially an algebraic addition or subtraction depending on whether they are moved in a forward or backward direction. In other words, once the correction for the residual error of phase shifter 23 is established and maintained at all times, it is immaterial what arbitrary reading is given to the coarse and ne scales 31 and |48, respectively, at a given instant.

Fig. shows a modification of Fig. 12 in that the former provides a correction curve |12 which is longer than but similar to the correction curve |51 in Fig. 12 and Which may be useful in certain cases. Thus, Fig. 15 provides a correction curve |12 which may be contained on reels in the manner of lm and which may be any length whereas the correction curve |51 according to Fig. '12

is fixed n length by the periphery of transparent drum |33. Referring to Fig. 15, engaging spur gears |66 and |61 are formed with a predetermined ratio and are substituted for the transparent drum |33 in Fig. 12. A shaft |68 has one end mounted in the sp-ur gear |61 and its opposite end rigidly attached to transparent drum |69 which is similar to the transparent drum |33 in Fig. 12. Two sets of sprocket teeth |10 of the usual structure are disposed on the periphery of transparent drum |69 adjacent the opposite ends thereof, and are adapted to accommodate the two spaced sets of familiar apertures formed adjacent longitudinal edges of a lm |1| carrying a correction curve |12 for the phase shifter 23. The remaining elements in Fig. 15 are identical with corresponding elements in Fig. 12. The film |1| in Fig. 15 may be of the endless type or stored in magazines as disclosed in the Slonczewski patent, supra.

Fig. 16 is an alternate embodiment of the arrangement of Fig. 12 in that the former includes a linear movement for effecting phase shift whereby the correction curve for residual error is caused to move in a linear direction. The arrangement of Fig. 16 may be substituted in Fig. 1 between the lines X-X and Y-Y. Referring to Fig. 16, a phase shifter 200vcomprises a pair of conductors 20|, 20|, a slider pick-up 202, a termination 203, and an amplifier 204. Attached to slider pick-up 202 is one end of a pinion rack 205 whose opposite end is connected to a transparent member 206 on the surf-ace of which is mounted correction curve 261, the latter being similar to correction curve |51 in Fig. 12. Immediately in front of the transparent member 206 is scale |48 which is mounted on a gear 209 meshing with gear 2|0. The latter meshes with gear 2| attached to one end of shaft 2 2 whose opposite end carries a pinion 2 3 meshing with pinion rack 205. Intermediate transparent member 206 and scale |48 is transparent window |62 provided with a frosted surface |6|. Light source |58 and lens |59 .are positioned. rearwardly of transparent member 206. As the slider pick-up is moved along the conductors 20|, a portion 2 3 of correction `curve 201 is projected onto the frosted surface |6| to constitute a moving index f-or the scale |48, similarly to the projected light beam |63 in Fig.,12. In Fig. 16, it will be understood that phase shifter 200 is merely illustrative of one device for obtaining variable phase shift by linear motion of a controlling slider pick-up 202, and alternate devices will be immediately suggested to those skilled in the art.

Fig. 17 shows another arrangement utilizing an optical device for providing a movable index for a calibrated scale, and comprises a phase shifter 220 mounted on one end of shaft 22| which also includes gear 222 and transparent disk 223 carrying a correction curve 224, similar to correction curve |51 in Fig. 12. Meshing with gear 222 is a gear 225 attached rigidly'to one end of shaft 226 whose opposite carries a calibrated scale 221. Positioned adjacent the latter scale is a transparent window 228 having a frosted surface 229. Associated with the window 228 is a light source 230 and lens 23|. If desired, the scale 221 may include knob 232 connected to a clutch device, not

Y shown, but similar to the clutch device associated with the scale |148 in Fig. 12 as previously described. In Fig. 17, scale 221 is similar to coarse scale 31 in Fig. 12 so that the movable index or projected light beam 233 in Fig. 17 on frosted surface 229 is similar to the projected light beam |63 in Fig. 12. Obviously, therefore, correction curves for the residual error of the phase shifter may y.bebassociated-` .with both the.. coarse-andine scales thereof where desired.

Eig. 18=shows an optical. arrangement .for correcting. deviations from. a .predetermined .scale Whichamay. or may. notaba linearI andwhichmay belof a .type disclosedinthe .patent of: T. Slonc- Zewski No. 2,058,641, issued October27, 1936.. Referringto Fig. 18, a lmldacontains a: predetermined scale 241| and; a. .correctionV curve 242., similar. .to .correction .curve |57.v in Fig.. 12. .Immediately behind thepredetenmined .scale 24|.is atransparentwindow. 243..vvith .afrostednsurface 2.44'. Associated. With..theY foregoing. iswan optical system245 which.. comprises alight .source 2:15-, lens 24.1', al1-degree .prisma 24 8, .dove prism.. 249., and:.90;;degree.prism 250. AsshowninFig 13, the=..dove. prismI .2149... is ,tiltedz at.. 45 1 degrees, thus rotating the- .beam of. lightpassing. therethrough by. 90'1degrees aboutlthezaxis thereof. As. a consequence, a.. portion..'252i of correction .curve- 24.2. is .projected.ontothefrosted surface bulto intersect base line 25|. of. thepredetermined .scale 24| therebycOnStituting.a.movable index for. thezlatterscaleeas the..lm.2..4\is,moved;. Obviously., the .predetermined scale 2.4.1.. and correction curve 242 may be formed on differentcfllm,.disposedindife ferent vplanesor. at right.angles, .moving together; andalternate optical .systems ofwell-known types couldbe substituted for theoptical. system 2.45.

. ...What isclaimedisl:

lnncombnation.. withV apparatus.. calibrated over; a preselected range andincluding. a predetermined.. scale.. formed. substantially.. on. a- .plane surface.. said apparatus.. being. operable over.. said range. and deviating. from, said.. scaleat at..least one. point insaidrange, .meanscontrolled by said .apparatus .over said. range. for. v.indicatingthe deviation. of. said .apparatus from said .scale,. said ,mansgcomprisinga correctvecurveshowing. the deviation. of,` said.apparatusiromsaid scale, and .optical .means forproi ectingdifferent portions of Said: Curve ...ont.o.. another. substantially. planev .surface positioned. inproximityof. saidscale, said plane.;s.urf.ace forsaidscale andsaidplane surface f orI saidprojected curve. portionsbeing. effectively disposednbne. .plane asregard-s readings .of said scale assaidapparatus. is operatedf.v over; said range, .sadproj ectedcorrective .curve portions .indicating .thedeyiation oisaidapparatus from .said scale: oversaidrangeand.thereby constituting a movable.. index. against .whichsaid scale .iss read over the calibrated range of said apparatus...

2.. combination. with. apparatus.. calibrated over ayppreselecte.d..range. and.. including. alinear SOMS, Sad.. apparatus.. being. operable .,over.. said range and .deviating frbm.. said. scale. at.. at.` least one point in said..range, .means operable by. said apparatusfor providing amovableindex .for said scale whereby the; deviaticnbf. said.. apparatus from said scale is indicated, andiclutchv means for normally .connecting said. scale tosaid. apparatus, said. clutch, means being. operable .to disengage said scale, from said apparatus for... initially es.- tablishing, an arbitrary -readingonsaid scale-.with reference. to. said movable index and therebyf-with reference` to `thedeviationof .said apparatus.

3. In a` phase. shifting`r apparatus. includinga shaft for varying the phase shifting .characteristic. of vsaid apparatus during the .calibration .thereofy .over -a preselected range, a. linearscale for; said apparatus, andi a.A movableindex for sinds-cale comprising clutch, means. for.y connecting said scale. to said shaft, a correction. curve representing; the residual error ofsadapparatusand actuable. under controlrof said shaft .ina predetermined. fixed relation. With .referencethereto, -and* optical Ameans for. .projecting successive portions ofsaid correction curve in proximity of .saidscale so .thatsaid scaleis .read against saidl projected curve. portions .over the. calibrated range. of:v said apparatus, said.. proj ected .curve .portions .moving amounts .correspondingto the residual.. errory of said'.- apparatus thereby constituting a .movable indexfor. said scale. over the.. preselected cali bratedrangegcfsai-d apparatus, said clutch means .being..operable...to adJ'uStsaids-caleto any. desired .initialg reading. with.. relation to the pro-.- jectedcurve portions andtherebywithrelation'to anyinitialposition of.. saidshaft. andssaid. correctiontcurve.

. 4. In.. phaseshifting.. apparatus.. calibratediony a linear. scale .over a. preselectedrange. and includ.- ing differentamounts.of.residual.error thereoven said-scale lying. substantiallyinone plane, a mov.- able.. index for.. representing. said. resi-dual error `over said :.preselected .range relativeto .said `Scale, said Aindex. .comprising a correction: curve repre: senting .the residual. error. of said.. apparatus. over the preselected .rangeof calibration andactuable by.. said apparatus, alight sensitive. surface .dis- .posed adj acent said. scale, and. optical means .for projecting successive portions of..said.curve onto said surface. and; into. a...plane thereofwhichis effectively. coincident..with..the plane..of.said: scale as regardsreadings. thereof; said proj ectedcurve portions. moving on.-.said..surface amounts corresponding.. tothe residual; error of. saidv apparatus thereby constituting a movable index I'or repre- .senting .the aresiduaierrorof .said apparatus.

.5. .in phase shifting` apparatus.; comprising. a shaftforoperating saidfapparatus .through apre- .detcrminedrange ofgphase shift, said apparatus having.;diferentamcunts of.. .residual error over sai ;l ..calibration,` a` linear scaleconnected-.to said shaft anddisposed.substantially in one '.plane, a movablefindex for representing. theresidual error of Said... apparatus..thrbuglrsaid.calibration, .said index comprising l transparent means. connected `fixedly;tusaid shaft. and .actuable thereby, .means .mounted on. Said transparent. means. and. containing a. transparent.. correctioncurve for.. said residual; er101,.,said.. correction .means being f predetermingedly positioned on... said;..tr.ansparent meansin relation'to theresi-dualerrorof said apparatus; a. screen disposedu in proximityof said Scale, and-having a.. surface .positioned ...substantially in lthe plane. thereof...andiopticalmeansfor projetingga beam of .light throughfsuccessive portions of said transparentzmeans; andzsaidvcorrec- 'tion curve Vand-onto said. screen surfaceso that said. scale is. read;v against said. .projected light beamf substantiallygrin one; plane, said .light movingg-.on saidv screen .surface to .represent the' resid- -ual .errorofsaidapparatus .through its-calibration thereby. constituting .a..movable Vindexforv said scale..

In Jphase. shifting apparatus comprising; a shaft .for :actuatingsai-d'. apparatus overV a pre:- determined. calibrated. .rang-e, Vsaid-apparatus .tending tospossess different-amounts ofI residual error.- fcr. different positions of Isaidshaftover said range ,1 andV afpair of scale f orindi-cating theY phase shift -of- Asaid I apparatus, meansV lfor :automatically compensating said-'apparatusr for the residual error therein,- saidmeans-comprising one of'said scalescalibrated with a preselected number of Llinear-rivisions, the-otherof' said scales. being linearly calibrated on aV plane surface with one division of-said one scale, clutch means for operatively connecting said-one scale to saidY shaft; 

